What is expand (e^{2t}+e^{-t})^2 ?

The solution to expand (e^{2t}+e^{-t})^2 is e^{4t}+2e^t+e^{-2t}

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expand (e^{2t}+e^{-t})^2

expand

(e^{2 t} + e^{- t})^{2}

e^{4 t} + 2 e^{t} + e^{- 2 t}

Solution steps

(e^{2 t} + e^{- t})^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = e^{2 t}, b = e^{- t}

= (e^{2 t})^{2} + 2 e^{2 t} e^{- t} + (e^{- t})^{2}

Simplify

(e^{2 t})^{2} + 2 e^{2 t} e^{- t} + (e^{- t})^{2} : e^{4 t} + 2 e^{t} + e^{- 2 t}

= e^{4 t} + 2 e^{t} + e^{- 2 t}

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What is expand (e^{2t}+e^{-t})^2 ?
The solution to expand (e^{2t}+e^{-t})^2 is e^{4t}+2e^t+e^{-2t}